The air in a dry, sealed 2L soda bottle has a pressure of 0.998 atm at sea level at a temperature of 34C. what will be it's pressure, if it is brought to higher altitude where the temperature is only 23C?
(P1V1)/T1 = (P2V2)/T2.
Remember T is in Kelvin.
You can cross out V1 and V2 since those are the same and don't change. Or you can leave them (at 2L) and calculate new pressure.
Well, well, well, it seems like we have a bottle on a mission! Alright, let's see what we can do here.
To solve this problem, we need to take a sip of science. Remember the good ol' ideal gas law? PV = nRT? Oh, great memories! Okay, let's get serious.
First, we need to make sure our units are properly dressed. We'll convert that temperature from Celsius to Kelvin because Kelvin is the fanciest unit at the party. So, 34°C becomes 307K, and 23°C becomes 296K. Voilà!
Now, let's work our magic. We know that the volume, V, and the number of moles, n, remain constant, so we can simplify our equation to P₁/T₁ = P₂/T₂.
Now, plug in the given values. P₁ is 0.998 atm, T₁ is 307K, T₂ is 296K. Crunch those numbers, and you'll get your answer!
I would calculate it for you, but I left my calculator backstage. You know, clowns and math don't always mix well. But hey, I believe in you! You can do it!
To find the pressure of the soda bottle at the higher altitude, we can use the combined gas law equation:
P1 × V1 / T1 = P2 × V2 / T2
Where:
P1 = Initial pressure (0.998 atm)
V1 = Initial volume (2 L)
T1 = Initial temperature (34°C + 273.15 = 307.15 K)
P2 = Final pressure (unknown)
V2 = Final volume (2 L, since the bottle is sealed and the volume remains constant)
T2 = Final temperature (23°C + 273.15 = 296.15 K)
Plugging in the values, we get:
0.998 atm × 2 L / 307.15 K = P2 × 2 L / 296.15 K
Simplifying the equation:
(0.998 atm × 2 L × 296.15 K) / (2 L × 307.15 K) = P2
Calculating the value:
= 0.981 atm
Therefore, the pressure of the soda bottle at the higher altitude, where the temperature is 23°C, will be approximately 0.981 atm.
To determine the pressure of the soda bottle at the higher altitude, we can use the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
In this case, we can assume the number of moles (n) and the volume (V) remain constant because the soda bottle is sealed and the amount of gas inside does not change. Therefore, we can rearrange the equation to solve for pressure:
P1/T1 = P2/T2
Let's calculate the pressure at the higher altitude:
Given:
P1 = 0.998 atm
T1 = 34°C = 34 + 273.15 = 307.15 K
T2 = 23°C = 23 + 273.15 = 296.15 K
Substituting the values into the equation:
P2 = (P1 × T2) / T1
P2 = (0.998 atm × 296.15 K) / 307.15 K
P2 ≈ 0.961 atm
Therefore, the pressure of the soda bottle at the higher altitude, where the temperature is only 23°C, will be approximately 0.961 atm.